Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons
Publication Date
September 25, 2009
Journal
PLOS Computational Biology
Authors
Sami El Boustani, Olivier Marre, Sébastien Béhuret, Pierre Baudot, et al
Volume
5
Issue
9
Pages
e1000519
DOI
https://dx.plos.org/10.1371/journal.pcbi.1000519
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000519
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/19779556
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2740863
Europe PMC
http://europepmc.org/abstract/MED/19779556
Web of Science
000270800100008
Scopus
70349667213
Mendeley
http://www.mendeley.com/research/networkstate-modulation-powerlaw-frequencyscaling-visual-cortical-neurons
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Mendeley | Further Information

{"title"=>"Network-state modulation of power-law frequency-scaling in visual cortical neurons", "type"=>"journal", "authors"=>[{"first_name"=>"Sami", "last_name"=>"El Boustani", "scopus_author_id"=>"22733728700"}, {"first_name"=>"Olivier", "last_name"=>"Marre", "scopus_author_id"=>"26434413400"}, {"first_name"=>"Sébastien", "last_name"=>"Béhuret", "scopus_author_id"=>"35078236000"}, {"first_name"=>"Pierre", "last_name"=>"Baudot", "scopus_author_id"=>"6701577099"}, {"first_name"=>"Pierre", "last_name"=>"Yger", "scopus_author_id"=>"15043413100"}, {"first_name"=>"Thierry", "last_name"=>"Bal", "scopus_author_id"=>"6701842488"}, {"first_name"=>"Alain", "last_name"=>"Destexhe", "scopus_author_id"=>"7006034474"}, {"first_name"=>"Yves", "last_name"=>"Frégnac", "scopus_author_id"=>"7003769970"}], "year"=>2009, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"70349667213", "doi"=>"10.1371/journal.pcbi.1000519", "issn"=>"1553734X", "pui"=>"355378049", "isbn"=>"1553-734X", "pmid"=>"19779556", "scopus"=>"2-s2.0-70349667213"}, "id"=>"4db010a3-73ee-3e85-82d1-26cbf3317e3a", "abstract"=>"Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the \"effective\" connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI.", "link"=>"http://www.mendeley.com/research/networkstate-modulation-powerlaw-frequencyscaling-visual-cortical-neurons", "reader_count"=>110, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>11, "Researcher"=>33, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>33, "Student > Master"=>9, "Other"=>5, "Student > Bachelor"=>6, "Lecturer"=>4, "Professor"=>4}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>11, "Researcher"=>33, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>33, "Student > Master"=>9, "Other"=>5, "Student > Bachelor"=>6, "Lecturer"=>4, "Professor"=>4}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Engineering"=>9, "Mathematics"=>1, "Agricultural and Biological Sciences"=>52, "Medicine and Dentistry"=>7, "Neuroscience"=>13, "Physics and Astronomy"=>14, "Psychology"=>4, "Social Sciences"=>2, "Computer Science"=>4}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>9}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>7}, "Neuroscience"=>{"Neuroscience"=>13}, "Social Sciences"=>{"Social Sciences"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>14}, "Psychology"=>{"Psychology"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>52}, "Computer Science"=>{"Computer Science"=>4}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>4}}, "reader_count_by_country"=>{"Hungary"=>1, "United States"=>2, "United Kingdom"=>2, "Switzerland"=>1, "Spain"=>1, "Canada"=>2, "Austria"=>1, "Netherlands"=>1, "Belgium"=>1, "Denmark"=>1, "Italy"=>1, "France"=>7, "Germany"=>3}, "group_count"=>4}

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/882641"], "description"=>"<p>The synchrony percentage has been fixed to 6% in each simulation. <b>A</b> The relative frequency-scaling exponent (color-coded) for and ranging from 0 to 1 without any correlation between excitatory and inhibitory inputs. <b>B,C</b> Same graph but with 40% (panel B) and 80% (panel C) correlation between excitatory and inhibitory inputs. In each graph, the excitatory input has a stronger influence on the output frequency-scaling exponent than the inhibitory input. <b>D</b> For , the output frequency-scaling exponent modulation is represented according to different correlation levels.</p>", "links"=>[], "tags"=>["frequency-scaling", "exponent", "excitatory", "inhibitory", "parameters"], "article_id"=>553091, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g006", "stats"=>{"downloads"=>2, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_values_of_the_frequency_scaling_exponent_for_different_excitatory_and_inhibitory_parameters_and_/553091", "title"=>"Relative values of the frequency-scaling exponent for different excitatory and inhibitory parameters and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:51:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/882417"], "description"=>"<p><b>A</b> Simple representation of the conductance generator. At each time step , with a probability proportional to the firing rate , k+1 neurons emit a spike synchronously. These spikes are then conveyed to the postsynaptic neuron with different delays, distributed according to a power-law probability density function (red curves). The arriving spikes then trigger post-synaptic conductances of exponential form (green curve, synaptic time course). The resulting conductance trace (green trace) has a PSD (blue curve) with a frequency power-law scaling behaviour. The analytical relation between the Fourier transform of the delay distribution and the PSD is given above the graphs. <b>B</b> The resulting synaptic conductance is then injected either in a model of single neuron or in a biological neuron through dynamic-clamp (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000519#s4\" target=\"_blank\">Materials and Methods</a>). In both cases, the resulting membrane potential is measured and the corresponding PSD is estimated.</p>", "links"=>[], "tags"=>["synchrony", "generator", "corresponding", "conductance", "injection"], "article_id"=>552869, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g004", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Conceptual_scheme_of_the_synchrony_generator_model_and_the_corresponding_conductance_injection_in_model_and_in_vitro_neurons_/552869", "title"=>"Conceptual scheme of the synchrony generator model and the corresponding conductance injection in model and <i>in vitro</i> neurons.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:47:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/882839"], "description"=>"<p>These controls were performed with integrate-and-fire neurons (left column), Hodgkin-Huxley neurons (middle column) and with biological neurons during <i>in vitro</i> experiments (right column). The synchrony percentage was kept at 6% and there was no correlation between excitatory and inhibitory synaptic inputs. For the <i>in vitro</i> experiments, each light line represents a cell, for which ten trials have been repeated with the same parameters. Error bars are the standard deviation over the trials. The bold line represents the average across cells and trials. Note that the reference value subtracted to each measured exponent is the one obtained when the input parameter to allow a direct comparison between models and <i>in vitro</i> data. <b>A</b> PSDs obtained for three values of . The modulation of the PSD slope is apparent. The absolute slope values are respectively (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000519#s4\" target=\"_blank\">Materials and Methods</a>): −3.35 −3.82 and −4.4 (integrate and fire, left); −3.35 −3.82 and −4.4 (Hodgkin-Huxley, middle); −3.28, −3.7 and −3.92 (<i>in vitro</i>, right). <b>B</b> For three values of , the modulation of the output frequency-scaling exponent according to the mean input firing rate per presynaptic neuron. <b>C</b> Same measures according to the postsynaptic resting membrane potential .</p>", "links"=>[], "tags"=>["frequency-scaling", "exponent", "changes", "frequencies", "resting", "membrane"], "article_id"=>553286, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g008", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_frequency_scaling_exponent_changes_for_different_input_frequencies_and_for_different_resting_membrane_potential_/553286", "title"=>"frequency-scaling exponent changes for different input frequencies and for different resting membrane potential .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:54:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/882525"], "description"=>"<p>Excitatory conductance and membrane potential are plotted in the left and right column respectively. <b>A</b> Illustration of the PSD modulation on a log-log scale for different values of the parameter ranging from 0 (light blue) to 1 (dark blue). <b>B</b> Variation of the output frequency-scaling exponent with the parameter, for different levels of synchrony. When 4% of the presynaptic neurons are synchronous, the relation is almost saturated. <b>C</b> The gating effect of synchrony. For three fixed values of  = 0.1, 0.5 and 0.9, the curves represent the modulation of the output frequency-scaling exponent according to percent synchrony.</p>", "links"=>[], "tags"=>["frequency-scaling", "exponent", "conductance", "membrane", "levels", "excitatory", "parameters"], "article_id"=>552970, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g005", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Variation_of_the_value_of_the_frequency_scaling_exponent_at_the_conductance_and_membrane_potential_levels_for_excitatory_input_only_as_a_function_of_the_parameters_and_synchrony_percentage_/552970", "title"=>"Variation of the value of the frequency-scaling exponent at the conductance and membrane potential levels for excitatory input only as a function of the parameters and (synchrony percentage).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:49:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/882196"], "description"=>"<p><b>A</b> Power spectral density (PSD) for a given cell in response to the four different stimuli presented in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000519#pcbi-1000519-g001\" target=\"_blank\">Fig. 1</a>. The traces have been normalized so as to obtain the same value at 40 Hz, for the sake of clarity.<b>B</b> Illustration of the linear fit between 75 and 200 Hz for the dense noise protocol. The power-law scaling region extends beyond those frequencies but is affected by synaptic filtering at low frequencies and by noise artefacts at high frequencies. <b>C</b> Frequency scaling exponent comparison between DG and NI stimuli for each cell. The error bars represent the standard error of the mean (SEM) on the estimation of the frequency-scaling exponent across the 10 repetitions for each stimulus. The black abscissa line indicates equality between the DG and NI condition. <b>D</b> Population analysis relative to the DN case. Each bar indicates the percentage of variation from the DN frequency-scaling exponent. The asterisks (*) indicate a significant difference over the population of cells between the frequency-scaling exponents in response to DN and a given stimulus (paired Wilcoxon test, ). The fourth bar represents the relative change between the spontaneous activity (SA) and the DN condition. <b>E</b> Comparison between the frequency-scaling exponent measured during NI stimulation and spontaneous activity (SA) for each cell. The black line indicates equality. <b>F</b> Same comparison than <b>E</b> between DG and SA.</p>", "links"=>[], "tags"=>["frequency-scaling"], "article_id"=>552651, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g002", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Change_of_frequency_scaling_according_to_visual_context_/552651", "title"=>"Change of frequency-scaling according to visual context.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:44:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/882740"], "description"=>"<p><b>A</b> Example of the FF changes as a function of time bin, for different input parameters . The resting potential has been set to −60 mV to ensure a large enough number of spikes. The synchrony parameter is fixed at 6%. <b>B</b> Relation between spiking and relative frequency-scaling exponents for different resting potentials ( = −65 mV, −62.5 mV and −60 mV). <b>C,D</b> Fano Factor frequency-scaling exponents as a bivariate function of excitatory and inhibitory and parameters, in the absence of excitatory-inhibitory correlation and for and −65 mV (C), and in the case of 40% of correlation and −62.5 mV (D). In this latter case, has been increased by a few mV to ensure a reasonable level of spiking activity.</p>", "links"=>[], "tags"=>["frequency-scaling", "exponent", "fano", "spike"], "article_id"=>553189, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g007", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relation_between_the_frequency_scaling_exponent_and_that_measured_from_the_Fano_Factor_FF_of_the_output_spike_train_/553189", "title"=>"Relation between the frequency-scaling exponent and that measured from the Fano Factor (FF) of the output spike train.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:53:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/437559", "https://ndownloader.figshare.com/files/437608", "https://ndownloader.figshare.com/files/437676", "https://ndownloader.figshare.com/files/437704"], "description"=>"<div><p>Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex <em>in vivo</em>, the power spectral density of V<em><sub>m</sub></em> activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the <em>in vivo</em> case, our <em>in computo</em> simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented <em>in vitro</em> by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These <em>in vitro</em> manipulations induced a modulation of the scaling exponent, similar to that observed <em>in vivo</em> and predicted <em>in computo</em>. We conclude that the frequency-scaling exponent of the V<em><sub>m</sub></em> reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI.</p></div>", "links"=>[], "tags"=>["network-state", "modulation", "power-law", "frequency-scaling", "cortical", "neurons"], "article_id"=>146254, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000519.s001", "https://dx.doi.org/10.1371/journal.pcbi.1000519.s002", "https://dx.doi.org/10.1371/journal.pcbi.1000519.s003", "https://dx.doi.org/10.1371/journal.pcbi.1000519.s004"], "stats"=>{"downloads"=>36, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Network_State_Modulation_of_Power_Law_Frequency_Scaling_in_Visual_Cortical_Neurons/146254", "title"=>"Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2009-09-25 01:44:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/882082"], "description"=>"<p><b>A:</b> Stimuli used in the <i>in vivo</i> experiments. From left to right: Drifting Grating (DG): a sinusoidal grating with optimal spatial frequency and orientation, drifting at optimal frequency; Grating & Eye Movements (GEM): the same grating animated by a trajectory simulating the dynamics of eye movements; Natural Image & Eye Movements (NI): a natural image animated by the same trajectory mimicking eye movements; Dense Noise (DN): a dense noise of high spatial and temporal definition. All these stimuli were full-field and presented monocularly in the dominant eye. <b>B:</b> examples of intracellular responses of the same cell to the NI (top trace) and the DG (bottom trace) stimuli (data from Baudot, Marre, Levy, Monier and Frégnac, submitted; Baudot et al., 2004; Frégnac et al., 2005).</p>", "links"=>[], "tags"=>["neuroscience/sensory systems", "neuroscience/theoretical neuroscience"], "article_id"=>552539, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g001", "stats"=>{"downloads"=>5, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Protocols_of_visual_context_dependence_/552539", "title"=>"Protocols of visual context dependence.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:42:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/882312"], "description"=>"<p><b>A</b> Schematic representation of the network structure and connectivity. The cortical (lower sheet, blue and red neurons) and thalamic input (upper sheet, yellow neurons) layer-like networks () face each other. The cortical neurons are locally connected together, according to a Gaussian distribution () and the retino-thalamic input projects its synaptic connections on the cortical layer through a narrower Gaussian distribution (). <b>B</b> Example of raster plots in the cortical layer in response to two thalamic input synchrony levels (top: synchrony of 0%; bottom: synchrony of 10%). <b>C</b> Mean firing rate (top) and coefficient of variation (bottom) of the cortical layer response to thalamic inputs of different synchrony levels. For each simulation, twenty neurons were randomly chosen among the network population to estimate error bars. <b>D </b> (top) and (bottom) frequency-scaling exponents as functions of the input synchrony. Bars indicate standard deviations of the scaling exponent values. <b>E</b> Averaged spatial cross-correlation between neuronal activities as a function of the distance between pairs of neurons, for different input synchrony levels, normalized by the total area of the distant-dependent cross-correlation function. Inset: same graph without the normalisation. <b>F</b> values of the frequency-scaling exponent as a function of the coefficient of correlation integrated over distance. Inset: values of the frequency-scaling exponent as a function of the correlation extent in the network activity (see text). The same results are shown in red for an infinite spread of the thalamic input.</p>", "links"=>[], "tags"=>["frequency-scaling", "recurrent", "inputs", "synchrony"], "article_id"=>552767, "categories"=>["Neuroscience"], "users"=>["Sami El Boustani", "Olivier Marre", "Sébastien Béhuret", "Pierre Baudot", "Pierre Yger", "Thierry Bal", "Alain Destexhe", "Yves Frégnac"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000519.g003", "stats"=>{"downloads"=>3, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Modulation_of_the_frequency_scaling_in_a_recurrent_network_model_with_inputs_of_variable_synchrony_and_spread_/552767", "title"=>"Modulation of the frequency-scaling in a recurrent network model with inputs of variable synchrony and spread.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-09-25 00:46:07"}

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Relative Metric

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